I know of someone who asked someone at BOS and they said you can enter any terminal with a boarding pass for any terminal. This has been used, for example, to get Pre-Check for UA in terminal A, and taking the A to C shuttle. (However, I have not personally tried this, just heard of other people both asking and successfully doing it.)
The fact that E has a lot of international shouldn't make a difference, and there are also domestic flights that leave from E.